In a bombshell ruling last week, Mr Bercow said the deal could not be voted on for a third time in the current parliamentary session unless there were significant changes from the version last defeated by the Commons.
One option being explored by the government was to introduce a ‘paving motion’ to override his ruling.
However, at the start of debate on alternative Brexit plans suggested by MPs, Mr Bercow ruled that out as an option for ministers, meaning a third vote may now be impossible.
The only change secured by the government has been the publication of additional assurances on the Irish border backstop, and a change in Brexit date agreed at a summit in Brussels last week.
Addressing MPs, Mr Bercow said: “In the course of answering questions following her statement [on Monday], the Prime Minister accepted this constraint, saying that ‘I am very clear about the strictures that Mr Speaker gave when he made his statement last week and, were we to bring forward a further motion to this house, we would of course ensure that it met the requirements he made.’
“I understand that the government may be thinking of bringing meaningful vote three before the house either tomorrow or even on Friday, if the house opts to sit that day.
“Therefore, in order that there should be no misunderstanding, I wish to make clear that I do expect the government to meet the test of change.
“They should not seek to circumvent my ruling by means of tabling either a notwithstanding motion or a tabling motion. The table office has been instructed that no such motions will be accepted.
“I very much look forward, colleagues, to today’s debate and votes which give the house the chance to start the process of positively indicating what it wants.”
The Government has said it will only bring a third ‘meaningful vote’ on the Brexit deal if it has enough support to pass, and has yet to convince its DUP allies to back the agreement.
However, a Downing Street spokesman said the necessary procedural steps would be taken so that parliament could sit to hold a vote on Friday - the last to secure a longer extension to Article 50, under the terms of the agreement reached in Brussels.
Meanwhile, Mr Bercow selected eight of sixteen alternative Brexit options for ‘indicative votes’ on Wednesday night.
In a historic move, MPs took control of the Commons order paper at the start of the week, and this afternoon confirmed a first round of votes as well as additional time on Monday for a ‘runoff’ involving the most popular Brexit options.